Magnetic-resonance transceiver-phased array that compensates for reactive and resistive components of mutual impedance between array elements and circuit and method thereof

ABSTRACT

There is provided a novel method and circuit of compensating for cross-talk between pairs of adjacent array elements of a transceiver phased array and double-tuned transceiver arrays for a magnetic resonance system using a resonant inductive decoupling circuit. The geometry and size of the resonant inductive decoupling circuit allows for the decoupling circuit to compensate for the cross-talk between array elements, including the reactive and resistive components of the mutual impedance while being sufficiently small to not distort a RF magnetic field of the array elements produced within a sample.

PRIORITY

The present application claims priority from Provisional Application No.61/625,196 filed Apr. 17, 2012, titled “Resonant Inductive Decouplingfor MRI Transceiver Phased Arrays to Compensate for both Reactive andResistive Components of the Mutual Impedance.” The application isincorporated by reference herein in its entirety.

GOVERNMENT RIGHTS

This invention was made with government support under Contract no.EB009871 and Contract No. EB011639 awarded by the National Institute ofHealth. The government has certain rights in the invention.

TECHNICAL FIELD

The present invention relates to decoupling methodologies and circuitsthereof for array elements of a magnetic-resonance transceiver phasedarray, and more particularly to compensating for cross-talk among thearray elements using a resonant inductive decoupling circuit.

BACKGROUND ART

Transceiver phased arrays (also referred to as transceiver surface-coilarrays) may improve transmission performance (B₁/√kW) and B₁ homogeneityfor magnetic-resonance head imaging up to 9.4 T (Tesla). To furtherimprove reception performance and parallel imaging, the number of arrayelements has to be increased with correspondent decrease of their size.With a large number of small interacting antennas, decoupling is one ofthe most challenging aspects in the design and construction oftransceiver arrays. Previously described decoupling techniques (forexample, using geometric overlap, inductive or capacitive decoupling)have generally focused on eliminating only the reactance component ofthe mutual impedance. These decoupling methods may limit the obtainabledecoupling by as much as −10 dB due to residual mutual resistance.

B₁ magnetic field homogeneity generally refers to the homogeneity orinhomogeneity of a B₁ magnetic field quantified by the standarddeviation of the amplitude of the B₁ magnetic field over a given region.The B₁ magnetic field refers to the time-varying magnetic fieldgenerated by an RF antenna and is applied perpendicularly to the B₀magnetic field to alter the orientation of the nuclear spins of thenuclei of interest in the sample. The B₀ magnetic field generally refersthe primary static magnetic field applied by a MR system to a sample.

At high magnetic field strengths, where the object size becomescomparable to the RF wavelength, increased RF inhomogeneity, decreasedtransmit efficiency (μT/√W), and increasing local specific absorptionrate (SAR) pose significant limitations for conventional single-channeltransmit volume coils. For example, for body imaging, such limitationsmay be observed at 3 T and above, and for head imaging, such limitationsmay be observed at 7 T and above.

SAR generally refers to the measure of the rate at which energy isabsorbed by the nuclei when excited to the B₁ magnetic field.Transmission efficiency generally refers to the intensity of the B₁magnetic field generated by a coil element expressed in a unit ofintensity (pT, μT, gauss, or Hz equivalent) as a function of the powerapplied to the RF coil to achieve that intensity.

To overcome these limitations, substantial effort has been focused onthe development of transceiver phased arrays consisting of multipleindependent (i.e. decoupled) RF antennas used simultaneously for bothtransmission and reception. Transceiver phased arrays provide improvedhomogeneity, enhanced transmit efficiency and decreased SAR through theuse of RF shimming and parallel transmission.

RF shimming has been described in Adriany et al, Transmit and receivetransmission line arrays for 7 Tesla parallel imaging. 53 MAGN. RESON.MED. 434-445 (2005); Mao et al, Exploring the limits of RF shimming forhigh-field MRI of the human head, 56(4) MAGN. RESON. MED. 918-922(2006); Ibrahim et al, Insight into RF power requirements and B1 fieldhomogeneity for human MRI via rigorous FDTD approach, 25(6) J. MAGN.RESON. IMAG. 1235-1247 (2007); Avdievich et al, Short Echo SpectroscopicImaging of the Human Brain at 7T Using Transceiver Arrays, 62 MAGN. RES.MED. 17-25 (2009); and Kozlov et al, Analysis of RF transmit performancefor a multi-row multi-channel MRI loop array at 300 and 400 MHz,Proceedings of the Asia-Pacific Microwave Conference, Melbourne,Australia 1190-1193 (2011).

Parallel transmission has been described in Katscher et al, TransmitSENSE, 49 MAGN. RESON. MED. 144-50 (2003); Zhu, Parallel excitation withan array of transmit coils, 51 MAGN. RES. MED. 775-784 (2004); and Zhanget al, Reduction of transmitter B1 inhomogeneity with transmit SENSEslice-select pulses, 57(5) MAGN. RESON. MED. 842-847 (2007).

Head arrays with surface coils as individual elements have beensuccessfully utilized at 7 T and above. These efforts are described inAvdievich et al, Short Echo Spectroscopic Imaging of the Human Brain at7T Using Transceiver Arrays, 62 MAGN. RES. MED. 17-25 (2009); Avdievich,Transceiver phased arrays for human brain studies at 7T, 41(2) APPL.MAGN. RESON. 483-506 (2011); Gilbert et al, A conformal transceive arrayfor 7 T neuroimaging, 67 MAGN. RESON. MED. 1487-1496 (2012); and Shajanet al, A 16-Element dual-row transmit coil array for 3D RF shimming at9.4 T, PROC. OF THE 20TH ANNUAL MEETING ISMRM, Melbourne, Australia 308(2012).

Conventional MR systems typically employ a single transmission coil, togenerate the RF magnetic field, commonly referred to as the B₁ magneticfield. At higher magnetic field strengths, the wavelength of the RFmagnetic field becomes comparable to the size of the sample (i.e. bodyimaging at 3T and above, head imaging at 7T and above). Also, withincrease in the B₀ magnetic field, the peak requirement for the B1magnetic field has to also substantially increase while the transmissionefficiency decreases. This result has been observed and described in “7vs. 4T: F power, homogeneity, and signal-to-noise comparison in heatimages,” Magn. Reson. Med. 46(1):24-30 (2001). Thus, at high magneticfield, it has been observed that a performance of a single transmissioncoil is significantly limited by increased RF inhomogeneity, decreasedtransmit efficiency (μT/W), and increased local specific absorption rate(SAR). Thus, transceiver phased arrays are more suited for highermagnetic field MR systems.

Transceiver phased arrays generally consist of multiple independent(i.e. decoupled) RF antennas configured to operate simultaneously forboth transmission and reception. More array elements may improve theefficiency and homogeneity of the RF magnetic field being transmitted,reduce the effects of localized absorption regions, improve thesensitivity of the reception, as well as provide for parallelmeasurements. Each array element generally interacts with neighboringand non-neighboring elements in the array. The interaction is referredto as cross-talk and affects the RF field profile of the array, thusdegrading the array transmission and reception performance, therebylowering the signal-to-noise ratio (SNR) of the transceiver phasedarray. Examples of transceiver phased array are provided in US PatentApplication, Publication No. 2012/0112748, titled “TransceiverApparatus, System, and Methodology For Superior In-Vivo Imaging of HumanAnatomy,” filed Aug. 18, 2011, by Hoby P. Hetherington, Jullie W. Pan,and Nikolai I. Advievich, which is incorporated by reference herein itis entirety.

Transceiver phased arrays may be used as conventional phased arrays forreception with the sensitivity of the receiver maintained. To providesufficient coverage of the entire object during transmission and highsignal-to-noise ratio (SNR) comparable with commercially availablemulti-channel receive-only arrays, the transceiver phased arrays mayinclude multiple rows of smaller RF elements. For example, two or threerows of eight elements (2×8 and 3×8) may be employed for a head-sizedarray.

To overcome these limitations, substantial effort has been focused onthe development of transceiver phased-arrays consisting of multipleindependent (i.e. decoupled) RF antennas used simultaneously for bothtransmission and reception. With a large number of interacting RFantennas, decoupling, i.e. eliminating the cross talk, is becoming oneof the most challenging and critical aspects in designing andconstructing transceiver phased arrays.

It is known in the art to decouple array elements (also referred to assurface coils) of transceiver phased arrays using inductive orcapacitive decoupling methodologies, thereby eliminating or reducingcross-talk. For certain geometries of individual antennas (e.g.overlapped surface coils) the cross-talk may include both reactive and asignificant resistive components. All previously developed decouplingmethods deal with eliminating only the reactive component of coupling(i.e. mutual inductance). Therefore, in these cases, use of anypreviously described decoupling schemes does not provide a completedecoupling of the array elements.

Compensating for both the resistive (real) and reactive (imaginary)components of the cross-talk may yield improved transceiver surface-coilarrays performance, thereby improving the sensitivity and imagingquality of the magnetic resonance system. Methods of decoupling thearray elements using a resonant inductive decoupling circuit thateliminates the reactive component of the mutual impedance between arrayelements are also known in the art.

Overlapping of adjacent array elements is a common inductive decouplingtechnique and enables larger and greater numbers of RF coils to be usedfor a given circumference of the array. This technique is described inRoemer et al, The NMR phased array, 16 MAGN. RESON. MED. 192-225 (1990);Kraff et al, An eight-channel phased array RF coil for spine MR imagingat 7 T, 44(11) INVEST. RADIOL. 734-740 (2009); and Keil et al,Size-optimized 32-channel brain arrays for 3 T pediatric imaging, 66MAGN. RESON. MED. 1777-1787 (2011), which are all incorporated byreference herein in their entirety.

Resonant inductive decoupling (RID) provides a way to compensate forboth the reactive and the resistive components of the mutual impedance,Z₁₂ (20). It also offers an easy way to adjust the decoupling, bychanging the resonant frequency of the decoupling circuit throughadjustment of a single variable capacitor. However, the placement andthe geometry of these RID elements are critical since the RF fieldgenerated by the RID can significantly alter the RF field of the array.

SUMMARY OF THE EMBODIMENTS

In a first embodiment of the invention, there is provided a novel methodof compensating for cross-talk between pairs of adjacent array elementsof a transceiver phased array for a magnetic resonance (MR) system. Thetransceiver phased array includes array elements circumscribing asample. In an embodiment, a method of operating a transceiver phasedarray decoupled using the illustrative embodiment is provided. Thetransceiver phased array is operated in the MR system to produce adataset of the sample. The dataset may be used to derive (i) an imageusing various described MR imaging modalities or (ii) spectroscopic datausing various measurement modalities described herein. The transceiverarray elements, i.e. RF antennas, may be configured as surface coilsused for both for transmission and reception of RF signals. Duringtransmission and reception, the pair of array elements has cross-talkcharacterized as mutual impedance therebetween, which may include bothresistive and reactive components.

The method includes providing a sample within the magnetic resonancesystem. Pairs of adjacent array elements of the transceiver phased arraymay be energized to cause transmission of a RF magnetic field (i.e., B₁magnetic field) and reception of a resonance signal from the sample.Each pair of the adjacent array elements may include a resonantinductive decoupling circuit that compensates for both the reactive andresistive components of the mutual impedance between each pair of arrayelements during transmission and reception. The method includesproducing the data set based on the received resonance signal.

The resonant inductive decoupling circuit inductively couples to thepair of array elements to compensate for both the reactive and resistivecomponents of the mutual impedance of the pair of array elements. Thecoupling is performed in a manner so as to not distort a RF magneticfield of the array elements produced in the sample.

The resonant inductive decoupling circuit may be configured such thatflux generated by the pair of array elements produces two currents ofopposing direction in the resonant inductive decoupling circuit, whichprovides conditions for compensation for both the reactive and resistivecomponent of the mutual impedance between the pair of array elements.

The resonant inductive decoupling circuit may consist of (i) two smalltwo-turn inductors, where each inductor is connected in series with eacharray element of the pair of adjacent array elements and (ii) anelectrically insulated resonant coil with a pair of two-turn windings,where each winding is coupled to each small inductor. Each of the twosmall inductors of the array elements and each of the pair of windingsof the resonant coil may have two to four turns.

The resonant inductive decoupling circuit may resonate at a resonantfrequency ω₀ sufficiently distant from a resonance frequency ω_(L) ofthe array elements to compensate for both the reactive and resistivecomponent of the mutual impedance between the pair of array elements.The difference between ω₀ and ω_(L), or frequency shift, may be equal to

${\frac{k}{2\eta}\frac{Q}{Q_{0}}\omega_{L}},$where k is the coupling coefficient between array elements of the pairof array elements, Q_(o) is a Q-factor of the resonant inductivedecoupling circuit, Q is a Q-factor of the array elements, η is a ratiobetween (i) a resistive component R₁₂ between the resonant inductivedecoupling circuit and the array elements and (ii) a resistance value Rof the array elements, and ω_(L) is the resonance frequency of the arrayelements. The resonant inductive decoupling circuit may have a geometryand size that produce a coupling coefficient k₀ with the array elementsufficiently large to provide for sufficiently large frequency shift (ordifference) between ω₀ and ω_(L). In an embodiment, the couplingcoefficient k₀ may be equal to

${k\sqrt{\frac{Q_{0}}{\eta\; Q}}},$where k is the coupling coefficient between array elements of the pairof array elements. The coupling coefficient may have a value greaterthan 0.08 to provide for the frequency shift of greater than 10% ofω_(L) to not distort a RF magnetic field of the array elements producedwithin a sample.

The size of the resonant inductive decoupling circuit may besufficiently small so as not to distort a RF magnetic field of the arrayelements produced within a sample. In an embodiment, the size of theinductors of the resonant inductive decoupling circuit is less thanthirty percent of the distance between the array elements and thesample.

In another embodiment of the invention, there is provided a transceiverphased array for a magnetic-resonance system. The transceiver phasedarray is adapted with a plurality of array elements configured tocircumscribe a sample. The plurality of array elements may beoverlapping or non-overlapping. Array elements, i.e., RF antennas, maybe configured for transmission of a RF magnetic field and reception of aresonance signal and may be configured as a surface coils. Adjacent pairof array elements may have cross-talk characterized as a mutualimpedance therebetween, which includes resistive and reactivecomponents.

The transceiver phased array includes a resonant inductive decouplingcircuit to cancel the cross-talk between the array elements. Theresonant inductive decoupling circuit is configured to inductivelycouple to a pair of adjacent array elements and compensates for thereactive and resistive components of the mutual impedance therebetween.The resonant inductive decoupling circuit is configured to inductivelycouple to the pair of array elements in a manner not to distort the RFmagnetic field of the array element produced within the sample. Inanother embodiment, the resonant inductive decoupling circuit is furtheremployed to inductively couple non-adjacent pairs of array elements.

The RID circuit may consist of (i) two small two-turn inductors, whereeach inductor is connected in series with each array element of the pairof array elements and (ii) an electrically insulated resonant coil witha pair of multi-turn windings, where each winding is coupled to eachsmall inductor. The two small inductors of the array elements and thepair of windings of the resonant coil may have two to four turns. Thetwo small inductors of the array elements and the pair of windings ofthe resonant coil may form a transformer.

In an embodiment, each of the inductors of the pair of array elementsmay be interleaved to the corresponding inductors of the resonantinductive decoupling circuit. In alternative embodiments, the inductorsof the pair of array elements may be placed alongside the correspondinginductors of the resonant inductive decoupling circuit. The inductors ofthe pair of array elements may be placed on the same side or theopposite side of corresponding inductors of the resonant inductivedecoupling circuit.

The resonant inductive decoupling circuit may be configured such thatflux generated by the pair of array elements produces two currents ofopposing direction in the resonant inductive decoupling circuit. The twocurrents compensate for both the reactive and resistive component of themutual impedance between the pair of array elements.

The resonant inductive decoupling circuit may resonate at a resonantfrequency ω₀ sufficiently distant from a resonance frequency ω_(L) ofthe array elements to compensate for both the reactive and resistivecomponent of the mutual impedance between the pair of array elements andnot distort a RF magnetic field of the array elements produced within asample. The difference between ωd0 and ω_(L), referred to as a frequencyshift, may be equal to

${\frac{k}{2\eta}\frac{Q}{Q_{0}}\omega_{L}},$where k is the coupling coefficient between array elements of the pairof array elements, Q_(o) is a Q-factor of the resonant inductivedecoupling circuit, Q is a Q-factor of the array elements, η is a ratiobetween (i) a resistive component R₁₂ between the resonant inductivedecoupling circuit and the array elements and (ii) a resistance value Rof the array elements, and ω_(L) is the resonance frequency of the arrayelements. The resonant inductive decoupling circuit may have a couplingcoefficient k₀ with the array element sufficiently large to provide forsufficiently large shift between ω₀ and ω_(L) while having a sizesufficiently small to not distort a RF magnetic field of the arrayelements produced within the sample. In an embodiment, the couplingcoefficient k₀ may be equal to

${k\sqrt{\frac{Q_{0}}{\eta\; Q}}},$where k is the coupling coefficient between array elements of the pairof array elements. The coupling coefficient may be greater than 0.08 toprovide for the frequency shift of greater than 10% of ω_(L).

The resonant inductive decoupling circuit may include a variablecapacitor to tune the resonant inductive decoupling circuit to resonateat the resonant frequency ω₀.

In another embodiment, a high-field multi-element multi-rowmagnetic-resonance transceiver-phased array is provided. The transceiverphased array includes a plurality of array elements arranged in multiplerows, including a first row of array elements and a second row of arrayelements. Each array element may have at least one adjacent arrayelement having mutual impedance therebetween. The multi-elementmulti-row transceiver phased array may include a plurality of resonantinductive decoupling circuit configured to decouple pairs of adjacentarray elements. Each resonant inductive decoupling circuit may consistof (i) two small inductors, each inductor connected in series with eacharray element of the adjacent pair of array elements and (ii) anelectrically insulated resonant coil with a pair of windings, eachwinding coupled to each small inductor. The two small inductors of thearray elements and the pair of windings of the resonant coil may havetwo to four turns. Each pair of the two small inductors of the arrayelements and the pair of windings of the resonant coil may form atransformer. The resonant inductive decoupling circuit is configuredsuch that it compensate for both the reactive and resistive componentsof the mutual impedance of each of the pairs of adjacent array elements.

In another embodiment, a double-tuned magnetic-resonancetransceiver-phased array is provided. The transceiver phased arrayincludes a plurality of array elements configured to resonant at twopre-specified frequency. The plurality of array elements may be arrangedto forms multiple rows, including a first row of array elements and asecond row of array elements, consisting of multiple array elements.

Each array element may have at least one adjacent array element havingmutual impedance therebetween. The transceiver phased array may includea plurality of resonant inductive decoupling circuit configured todispose between pairs of adjacent array elements. Each resonantinductive decoupling circuit may consist of (i) two small inductorsconnected in series with the array elements and (ii) an electricallyinsulated resonant coil with a pair of windings coupled to each arrayelement. The two small inductors of the array elements and the pair ofwindings of the resonant coil may have two-turns to four turns. The twosmall inductors of the array elements and the pair of windings of theresonant coil may form a transformer. The resonant inductive decouplingcircuit is configured such that it compensate for both the reactive andresistive components of the mutual impedance of each of the pairs ofadjacent array elements.

In an embodiment, the plurality of array elements of the double-tunedtransceiver phased array may include a set of single double-tuned coilresonating at two frequencies. In another embodiment, the plurality ofarray elements may include two sets of coils, each coil set configuredto resonant a different resonant frequencies. The first coil set may benested within the second coil set.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of embodiments will be more readily understood byreference to the following detailed description, taken with reference tothe accompanying drawings, in which:

FIG. 1 illustrates a transceiver phased array with resonant inductivedecoupling circuits to cancel cross-talk among the array elementsaccording to an illustrative embodiment.

FIG. 2 is an electrical diagram showing a resonant inductive decouplingcircuit inductively coupled to a pair of array elements.

FIG. 3 is an electrical schematic of a transceiver phased array withresonant inductive decoupling circuits according to an embodiment.

FIGS. 4A and 4B schematically illustrate a resonant inductive decouplingcircuit according to the illustrative embodiment.

FIG. 4C schematically illustrates an alternative arrangement of theresonant inductive decoupling circuit of FIG. 4A.

FIG. 4D schematically illustrates a layout of components of a resonantinductive decoupling circuit according to an embodiment.

FIGS. 4E and 4F are photographs of a resonant inductive decouplingcircuit of FIG. 4D.

FIGS. 4G-4H schematically illustrate layouts of components of a resonantinductive decoupling circuit according to an alternate embodiment.

FIG. 4I shows the front view of a resonant inductive decoupling circuitaccording to another embodiment.

FIG. 4J illustrates a layout of a 2×4 transceiver phased array decoupledwith resonant inductive decoupling circuits according to theillustrative embodiment.

FIG. 4K is a diagram illustrating the resonant inductive decouplingcircuit decoupling a pair of non-overlapping array elements.

FIG. 4L is a diagram illustrating the resonant inductive decouplingcircuit decoupling a pair of overlapping array elements.

FIG. 4M is a diagram of a pair of array element and a resonant inductivedecoupling circuit in relation to a sample.

FIGS. 5A-5C illustrate alternate resonant inductive decoupling circuits.

FIGS. 6A-6C illustrate other alternate resonant inductive decouplingcircuits.

FIG. 7 illustrates a resonant inductive decoupling circuit according toan alternate embodiment.

FIG. 8 is a diagram of a resonant inductive decoupling circuit, whichcompensates only for the mutual reactance and not the mutual resistance.

FIG. 9 illustrates a double-tuned resonant inductive decoupling circuitaccording to an embodiment.

FIG. 10 is an electrical schematic of a double-tuned resonant decouplingcircuit according to an embodiment.

FIG. 11 is an electrical schematic of a double-tuned resonant decouplingcircuit for a double tuned phased array.

FIGS. 12A and 12B illustrate a 16-element single-row transceiver phasedarray adapted with resonant inductive decoupling circuits according tothe illustrative embodiments.

FIG. 13 is a plot illustrating the dependence of the loaded Q-factorQ_(L) on the distance between a sample and the array elements.

FIG. 14 shows results for a ¹H 2-coil array decoupled with differenttypes of decoupling circuits.

FIG. 15A shows the axial B₁ maps obtained using a ¹H 2-coil array with(i) a resonant inductive decoupling shown in FIG. 5A and (ii) aconventional inductive decoupling.

FIG. 15B shows the B₁ ⁺ maps of individual array element decoupled withthe resonant inductive decoupling circuit according to the illustrativeembodiment.

FIG. 16A shows an image of a human patient scanned with a transceiverphased array decoupled with resonant inductive decoupling circuitsaccording to the illustrative embodiment.

FIG. 16B shows an axial B₁ ⁺ map corresponding to the scanned image ofFIG. 16A.

FIGS. 17A-C show axial B₁ ⁺ maps of individual array elements of a³¹P/¹H double-tuned array obtained decoupled with the resonant inductivedecoupling circuit according to the illustrative embodiment.

FIG. 17D shows axial B₁ ⁺ maps for individual array elements of thetransceiver phased array of FIGS. 12A and 12B configured with theresonant inductive decoupling circuit according to the illustrativeembodiment.

FIG. 17E shows an axial image of a human patient scanned using a 16-coil(1×16) overlapped array decoupled with resonant inductive decouplingcircuits according to the illustrative embodiment.

FIG. 17F shows a B₁ ⁺ map corresponding to the scanned image of FIG.17E.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

Definitions. As used in this description and the accompanying claims,the following terms shall have the meanings indicated, unless thecontext otherwise requires:

The term “distortion-less” refers to having minimally disturbed ordistorted the RF magnetic field of the RF surface coils.

The term “compensate” (such as in compensating for resistive componentof the mutual impedance between array elements) refers to canceling inits entirety, reducing to a lesser degree, and maintaining withoutincreasing.

The term “adjacent” refers to neighboring or being in direct proximityand without having another being disposed in between.

The term “sample” refers to an article, patient, or specimen beingimaged, scanned, or measured by a magnetic resonance system, includinghuman patients, biological samples and specimens, as well asnon-biological samples and articles.

The term “magnetic resonance system” refers to imaging modalities, suchas magnetic-resonance imaging (MRI), nuclear magnetic resonance imaging(NMRI), magnetic resonance tomography (MT), among others, as well asmeasurement modalities such as nuclear magnetic resonance (NMR)spectroscopy, and magnetic resonance spectroscopy (MRS). Additionalbackground information on magnetic resonance systems are described in USPatent Application (Publication No. 2012/0112748), incorporated byreference herein in its entirety. A large variety of differentassemblies and a wide range of alternative systems have been developedover time for performing magnetic resonance systems, and all of theseare well established and conventionally known in the technical field.The scope and diversity of these various developments are merelyexemplified and represented by U.S. Pat. Nos. 7,573,270; 7,501,823;7,358,923; 7,358,923; 7,345,485; 7,298,145; 7,285,957; 7,173,425;7,088,104; 7,088,100; 7,012,429; 6,940,466; 6,853,193; 6,771,070;6,552,544; 6,538,442; 6,107,798; 6,011,395; 5,998,999; 5,791,648;5,642,048; 5,610,521; 5,565,779; 5,483,163; 5,483,158; 5,473,252;5,461,314; 5,365,173; 5,243,286; 5,196,797; 5,185,575; 5,172,061;5,159,929; 5,081,418; 4,926,125; 4,918,388; 4,885,539; 4,879,516;4,871,969; 4,820,985; 4,788,503; 4,783,641; 4,780,677; 4,752,736;4,751,464; 4,737,718; 4,731,584; 4,725,780; 4,721,915; 4,129,822;4,320,342; and 4,638,253 respectively. The texts and figures of allthese U.S. patents are expressly incorporated by reference herein.

A “Type I” RID circuit is configured to couple with a pair of arrayelements in such a manner that the flux from the pair of array elementsinduces current of opposing direction that compensates for both thereactive and resistive component of the mutual impedance between thepair of array elements.

A “Type II” RID circuit is configured to couple with a pair of arrayelements in such a manner that the flux from the pair of array elementsinduces current in the same direction that compensates for the reactivecomponent of the mutual impedance between the pair of array elementswhile not compensating for the resistive component thereof.

The term “decoupling” refers to the process of eliminating a “crosstalk”or the energy transfer between two coupled antennas (such as arrayelements of a transceiver phased array) through the shared impedanceZ₁₂. The efficiency of decoupling as applied to transmission isevaluated by measuring the transmission parameter S₁₂, which is directlyrelated to the Z₁₂ value. In this sense, the resistive and reactivecomponent of the Z₁₂ simply describes the amplitude and phaserelationship of a signal propagating between ports of two coupledantennas. As applied to reception, the mutual resistance measuredbetween two coupled antennas is often related to their noisecorrelation. See, for example, Roemer et al, The NMR phased array, 16MAGN. RESON. MED. 192-225 (1990); and Wright, Full-wave analysis ofplanar radiofrequency coils and coil arrays with assumed currentdistribution, 15(1) CONC. MAGN. RESON. B: MAGN. RESON. ENG. 2-14 (2002).

FIG. 1 illustrates a transceiver phased array 100 with resonantinductive decoupling (RID) circuits 102 to cancel cross-talk among thearray elements 104 according to an illustrative embodiment. Thetransceiver phased array 100 is shown, for illustration, as part of amagnetic resonance imaging (MRI) system 106. In an MRI system, a magnet108 generates a generally uniform and static magnetic field (referred toas the B₀ magnetic field) along an axis of a sample 110. For MRIsystems, the B₀ magnetic field is generally oriented along alongitudinal axis of the patient. The B₀ magnetic field causes the netsummed nuclear spins of certain nuclei of the sample 110 to orient in aparticular direction. The transceiver phased array 100 is a secondseparate RF antenna (RF coil) assembly that generates a varying magneticfield (commonly referred to as the B₁ magnetic field) perpendicularly tothe B₀ magnetic field. The B₁ magnetic field varies at a frequency thatis absorbed by certain nuclei within the sample 110 (commonly referredto as the “resonant frequency” or the “Larmor frequency”) and istransmitted in pulses or bursts. The resonant frequency is typically inthe radio-frequency range (e.g., between 3 Hz and 3 Ghz), and thus theB₁ magnetic field and the associated transmission components aregenerally referred to as RF, such as “RF magnetic field” and “surface RFcoils.” During a pulse, a portion of the B₁ magnetic field is absorbedby the sample 110, which causes certain nuclei to transition to adifferent energy state with a different orientation. After the pulse,the nuclei attempt to regain the previous orientation and concomitantlyemit a different time-varying magnetic field, which is commonly referredto as a “resonance signal”. The resonance signal is also in the RFrange. The transceiver phased array 100 is a type of RF coil andincludes multiple distinct and independent surface coils as the arrayelements 104. The array elements are configured as RF antenna that mayoperate as (i) a transmitter to generate the B₁ magnetic field at theresonant frequency and (ii) a receiver to receive the resonance signal.Interaction (or coupling) between the array elements of the transceiverphased array 100 is generally referred to as “cross-talk” and degradesthe signal-to-noise performance of the array 100.

Each of the resonant inductive decoupling circuits 102 may include (i)two small inductors 122, 124 connected in series with the surface coils(i.e., array element 104) and (ii) an electrically insulated resonantcoil 103 with a pair of windings 112, 114 coupled to each surface coilof the array elements 104. The electrically insulated resonant coil 103may form two parallel loops 105, 107 in parallel with a capacitor 116.Capacitor 116 may comprise multiple capacitors in series or parallel toproduce the desired capacitance C₀. The electrically insulated resonantcoil produces a RF magnetic field which interacts with the magnetic fluxfrom the array element to generate two currents 118, 120 (referred asI₀) in opposing directions in the parallel loops 105, 107. The pair ofwindings 112, 114 of the resonant inductive decoupling circuit 102inductively couples to the small inductors 122, 124 of the arrayelements 104. Each of the resonant inductive decoupling circuits 102 maycancel the cross-talk between each pair of adjacent array elements 104by compensating for both the reactive X₁₂ and resistive components R₁₂of the mutual impedance Z₁₂ between each pair of array elements 104 andnot disturbed the RF magnetic field of the array elements 104.

The inventors have realized that to cancel the cross-talk and notdisturb the RF magnetic field of the array elements, the resonantinductive decoupling circuit 102 must satisfy two requirements. First,the resonant frequency of the resonant inductive decoupling circuit 102has to be sufficiently lower than the resonant frequency of the arrayelements 104 to minimize the interactions between the resonant inductivedecoupling circuit 102 and the array elements 104. The interactionrelates to the changing frequency dependence of current I₁, I₂ in thearray elements 104 and the RF magnetic field generated by the resonantinductive resonant circuit 102. To produce a sufficiently largedifference between the resonant frequencies of the resonant inductivedecoupling circuit and the resonant frequency of the array elements(frequency shift), the coupling between the array elements 104 and theresonant inductive decoupling circuit 102 has to be sufficiently large.Second, all inductors forming RID circuits have to be physically smallto not add to, thereby changing or distorting, the B₁ magnetic field ofthe array elements 104.

In the presence of a sample, the mutual impedance Z₁₂ may include asubstantial resistive component R₁₂ due to common current paths betweenthe pair of array elements within the sample. It has been shown thatadjacent overlapped surface coils under loading can generate substantialmutual resistance R₁₂. See, for example, Roemer et al, The NMR phasedarray, 16 MAGN. RESON. MED. 192-225 (1990); and Wright, Full-waveanalysis of planar radiofrequency coils and coil arrays with assumedcurrent distribution, 15(1) CONC. MAGN. RESON. B: MAGN. RESON. ENG. 2-14(2002).

In FIG. 1, the transceiver phased array 100 is shown with sixteennon-overlapping array elements arranged in a single row where each ofthe array elements 104 overlaps with a neighboring array element. Ofcourse, additional rows may be employed that are non-overlapping oroverlapping, and each of the array elements 104 may overlap with morethan one neighboring array element. The array elements 104 are organizedin a unified assembly and are collectively positioned as an aggregate ina pre-defined arrangement. In the transceiver phased array, loops of theRF current may be normally positioned parallel to the surface of thearray holder which circumscribes the sample. This orientation of thearray elements has been demonstrated to minimize the mutual inductivecoupling between elements of the array and simplifies the decoupling bylimiting the significant coupling to only adjacent elements. See, forexample, Tropp, Mutual Inductance in the Bird-Cage Resonator, 126 J.MAGN. RESON. 9-17 (1997).

FIG. 2 is an electrical diagram showing a resonant inductive decouplingcircuit 102 inductively coupled to a pair of array elements 104according to the illustrative embodiment. The resonant inductivedecoupling circuit 102 may be modeled as a circuit with two loops 202,204 in a “butterfly configuration” that produce two opposite currentsI₀. This topology of resonant inductive resonant circuit 102 may bereferred as a “Type I RID circuit.” The resonant inductive decouplingcircuit 102 has a resistance R₀ and a capacitance C₀. The loops 202, 204inductively couple to corresponding surface coils 206, 208 of the arrayelements 104 (labeled as “Coil#1” and “Coil#2”). The surface coil 206 ismodeled as a circuit with resistance R and inductance L that producescurrent I₁ when voltage V₁ is applied. Similarly, the surface coil 208is modeled as a circuit with resistance R that produces a current I₂when voltage V₂ is applied. The mutual impedance Z₁₂ between the surfacecoil 206 and surface coil 208 may be expressed as Z₁₂=jωM+R₁₂ where jωMrefers to the reactive component and R₁₂ refers to the resistivecomponent.

Equation 1 is the Kirchhoff equation of the three-circuit resonantsystem shown in FIG. 2.

$\begin{matrix}{\begin{pmatrix}V_{1} \\0 \\V_{2}\end{pmatrix} = {\begin{pmatrix}Z_{1} & {j\;\omega_{L}M_{0}} & {{{- j}\;\omega_{L}M} + R_{12}} \\{j\;\omega_{L}M_{0}} & Z_{0} & {{- j}\;\omega_{L}M_{0}} \\{{{- j}\;\omega_{L}M} + R_{12}} & {{- j}\;\omega_{L}M_{0}} & Z_{2}\end{pmatrix}\begin{pmatrix}I_{1} \\I_{0} \\I_{2}\end{pmatrix}}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

Z₀ is the impedances of the RID circuit, and Z₁ and Z₂ are thecorresponding impedance of the pair of array elements 104. M₀ is themutual inductance between the RID circuit 102 and the array elements104. For simplicity, the mutual inductance M₀ may be assumed to be equalfor each of the array elements 104 and the RID circuit 102. ω_(L) is theresonance frequency of the array elements 104, which may be assumed tobe the same among the array element 104 that form transceiver phasedarray 100.

As shown in Equation 1, the two currents 118, 120 (see FIG. 1) of theRID circuit 102 are opposite in direction. Specifically, the secondelement in the first row of Equation 1 (jω_(L)M₀) and the third elementin the second row (−jω_(L)M₀) have opposite signs. Same relationship isobserved for the first element in the second row and the second in thethird row.

Solving for V₁ and V₂ of Equation 1 yields Equation 2.

$\begin{matrix}{\begin{pmatrix}V_{1} \\V_{2}\end{pmatrix} = {\begin{pmatrix}{Z_{1} + \frac{\omega_{L}^{2}M_{0}^{2}}{Z_{0}}} & {{{- \left( {j\;\omega} \right)_{L}}M} + R_{12} - \frac{\omega_{L}^{2}M_{0}^{2}}{Z_{0}}} \\{{{- j}\;\omega_{L}M} + R_{12} - \frac{\omega_{L}^{2}M_{0}^{2}}{Z_{0}}} & {Z_{2} + \frac{\omega_{L}^{2}M_{0}^{2}}{Z_{0}}}\end{pmatrix}\begin{pmatrix}I_{1} \\I_{2}\end{pmatrix}}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

Near the resonance, Z₀ may be approximated asZ₀≈2jL₀(ω_(L)−ω₀)+R₀=2jL_(θΔ)ω+R0, where ω₀ is the resonance frequencyof the decoupling circuit and L₀ and R₀ are its inductance andresistance. To cancel the mutual impedance Z₁₂, the quantity

${{- j}\;\omega_{L}M} + R_{12} - \frac{\omega_{L}^{2}M_{0}^{2}}{Z_{0}}$may be obtained from the off-diagonal elements of Equation 2. Thequantity may be calculated as Equation 3, where R and L are theresistance and the inductance of the surface coils, and Q₀=ωL₀/R₀ andQ=ωL/R are corresponding Q-factors of the RID circuit 102 and the arrayelements 104.

$\begin{matrix}{{{{{- j}\;\omega_{L}M} + R_{12} - \frac{\omega_{L}^{2}M_{0}^{2}}{Z_{0}}} \approx {{{- j}\;\omega_{L}{kL}} + R_{12} - \frac{\omega_{L}^{2}{M_{0}^{2}\left( {R_{0} - {2\; j\;\omega_{L}L_{0}}} \right)}}{R_{0}^{2} + {4\left( {\Delta\omega}_{L} \right)^{2}L_{0}^{2}}}} \approx \approx {{{- j}\;\omega_{L}{kL}} + R_{12} - \frac{\omega_{L}^{2}k_{0}^{2}{{LL}_{0}\left( {R_{0} - {2\; j\;\omega_{L}L_{0}}} \right)}}{4\left( {\Delta\omega}_{L} \right)^{2}L_{0}^{2}}}} = {{{- j}\;\omega_{L}{L\left( {k - \frac{k_{0}^{2}}{2\xi}} \right)}} + R_{12} - {\frac{R}{4}\frac{k_{0}^{2}}{\xi^{2}}\frac{Q}{Q_{0}}}}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$

The relative frequency difference between ω_(L) and ω₀ (i.e., frequencyshift) is expressed in Equation 4.ξ=Δω/ω_(L)  (Equation 4)

Equation 3 accounts for M₀=k₀(LL₀)^(1/2) and M=kL, where k and k₀ arecorresponding coupling coefficients between array elements 104 andbetween an array element 104 and the RID circuit 102. For simplicity, R,L, and Q may be assumed to be the same for the pair of array elements104. From Equation 3, the resonant inductive decoupling circuit 102cancels both the real R₁₂ and imaginary M₁₂ components of the mutualimpedance Z₁₂ when Δω>0, which occurs when ω₀<ω_(L). To cancel themutual reactance, Equation 5 has to be satisfied.k ₀ ²=2kξ  (Equation 5)

To cancel the mutual impedance Z₁₂, the resonant frequency of theresonant inductive decoupling circuit 102 has to be relatively differentby ξ of Equation 6. ξ is typically greater than 0.1 (i.e., 10%) to notproduce distortions to the RF magnetic field of the surface coils withinthe sample. Of course, lower values of ξ (e.g., more than 0.05) may betolerated in applications where cross-talk is more tolerable.

$\begin{matrix}{\xi = {\frac{k}{2\eta}\frac{Q}{Q_{0}}}} & \left( {{Equation}\mspace{14mu} 6} \right)\end{matrix}$

Additionally, the coupling between each of the inductors 112, 114 of theRID circuit 102 and the corresponding inductors 122, 124 of the arrayelements 104 has to be sufficiently large (greater than 0.08) to providefor the frequency shift ξ of greater than 10% to not distort the RFfield of the array elements. The condition for the coupling coefficientk₀ is provided in Equation 7.

$\begin{matrix}{k_{0} = {k\sqrt{\frac{Q_{0}}{\eta\; Q}}}} & \left( {{Equation}\mspace{14mu} 7} \right)\end{matrix}$

η is a ratio of R₁₂/R. As a result, by varying the coupling coefficientk₀ and the relative frequency shift ξ, the resonant inductive decouplingcircuit 102 may cancel both the real R₁₂ and the imaginary X₁₂components of mutual impedance Z₁₂ between a pair of array elements 104.

FIG. 3 is an electrical schematic of the transceiver phased array 100with overlapping array elements 104 a, 104 b, 104 c, 104 d, 104 e. Thefigure illustrates the transceiver phased array 100 with resonantinductive decoupling circuits 102 a, 102 b, 102 c, 104 d configured todecouple pairs of adjacent array elements (pair 1: 104 a and 104 b; pair2: 104 b and 104 c; pair 3: 104 c and 104 d, and pair 4: 104 d and 104e). An array element 104 must be formed of a non-magnetic material, suchas copper, linked by tuning capacitors to provide a desired resonantfrequency. In addition to the decoupling network, the figure also showsthe matching network of the individual array elements

A separate common inductive decoupling circuit 302 a, 302 b, 302 c isemployed between non-adjacent array elements to cancel the mutualimpedance therebetween (e.g., between array elements 104 a and 104 c,between array elements 104 b and 104 d, and between array elements 104 cand 104 e). Of course, the resonant inductive decoupling circuit 102 maybe employed between the non-adjacent array elements to cancel the mutualimpedance.

FIGS. 4A and 4B schematically illustrate a resonant inductive decouplingcircuit 102 according to the illustrative embodiment. FIG. 4A shows thefront view of the RID circuit 102, and FIG. 4B shows the side view. Theresonant inductive decoupling circuit 102 includes inductors 112, 114that may be formed of turned-loops having two to four windings. It isdetermined that at higher resonant frequency (i.e., above 170 MHz), eachof the inductors 112, 114, 122, 124 may be formed with two-turned loops.At lower resonant frequency, more loops may be employed. For example fora 4T MRI system operating at 170 MHz or a 3T MRI system operating at 125MHz, the inductors 112, 114, 122, 124 may be formed with three orfour-turned windings.

The inductors 112, 114 form two parallel circuit loops joined by acapacitor 116 that may be mounted in a housing 402. The housing 402 mayprovide a structural member for the inductors 112, 114 to mount. The RIDcircuit 102 is configured to inductively couple to inductors 122, 124 ofthe array elements 104. The inductors 112, 114 of the RID circuit 102and the inductors 122, 124 of the array elements 104 may be configuredto interleave among each other.

FIG. 4C schematically illustrates an alternative arrangement of theresonant inductive decoupling circuit 102 of FIG. 4A. Rather than beinginterleaved, the inductors 122, 124 of the array elements 104 may bepositioned alongside the inductors 112, 114 of the RID circuit 102. Theaxis of the coils of the inductors 122, 124 may align with the axis ofthe inductors 112, 114. This embodiment may provide a lower couplingcoefficient k₀ value, but may be more convenient to layout. Of course,it should be appreciated that the inductors 112, 114 of the RID circuit102 and the inductors 122, 124 of the array elements 104 may partiallyinterleave among each other.

FIG. 4D schematically illustrates a layout of components of a resonantinductive decoupling circuit according to an embodiment. The capacitor116 of the electrically insulated resonant coil 103 is not shown forsimplicity. The inductors 112, 114 of the electrically insulatedresonant coil 103 are interleaved with the inductors 122, 124 of thearray elements 104. The axis of the inductors 112, 114 may substantiallyalign with the axis of the inductors 122, 124.

FIGS. 4E and 4F are photographs of a resonant inductive decouplingcircuit 102 of FIG. 4D according to an illustrative embodiment. In FIG.4E, the resonant inductive decoupling circuit 102 includes a variablecapacitor 116 that connects in parallel with two loops 112, 114, eachhaving an inductor. The two loops 112, 114 interleave with the twoinductors 122, 124 that are formed as part of the array elements 104.FIG. 4F shows the resonant inductive decoupling circuit 102 unassembledwith respect to the inductors 122, 124 of the array elements.

FIGS. 4G-4H schematically illustrate layouts of components of a resonantinductive decoupling circuit according to an alternate embodiment. InFIG. 4G, the inductors 112, 114 of the electrically insulated resonantcoil 103 are positioned alongside the inductors 122, 124 of the arrayelements 104. The axis of the inductors 112, 114 may substantially alignwith the axis of the inductors 122, 124. The inductor 122 and inductor124 may be positioned on opposite sides of the electrically insulatedresonant coil 103. Alternatively, as shown in FIG. 4H, the inductor 122and inductor 124 may be positioned on the same side in relation to theelectrically insulated resonant coil 103.

It should be appreciated that the electrically insulated resonant coil103, as shown in FIGS. 4D, 4G, and 4H, illustrates its layout inrelation to the inductors 122, 124 of the array elements 104. As such,details of the circuitry of the electrically insulated resonant coil103, including the capacitor 116, are not shown.

In an embodiment, the RID circuit 102 may be constructed having a 3 mm(millimeter) inner diameter using 20-gauge (i.e., diameter of 0.8 mm)magnet wires. Of course, other wire size and dimensions may be employedto provide a coupling coefficient k₀ greater than 0.08. The surfacecoils of the array elements 104 may be formed using 5 mm copper tape andform an overlap of 12 mm among the array elements 104.

In such a configuration, the proximity of the next nearest array element(i.e. Δn=2) resulted in mutual inductive coupling of ˜5 nH (k˜0.03).This coupling was eliminated by the use of conventional non-resonantinductive decoupling as shown in FIG. 3 and described in Avdievich etal, Short Echo Spectroscopic Imaging of the Human Brain at 7T UsingTransceiver Arrays, 62 MAGN. RES. MED. 17-25 (2009); and Avdievich,Transceiver phased arrays for human brain studies at 7T, 41(2) APPL.MAGN. RESON. 483-506 (2011), which are incorporated by reference hereinin their entirety. To decrease radiation losses, a shield (50 μmpolyamide film with a 5 μm copper layer, Sheldahl, Northfield, Minn.)was placed 4 cm away from the array elements 104. See, for example,Harpen, Radiative losses of a birdcage resonator, 29(5) Magn Reson Med.713-716 (1993), which is incorporated by reference herein in itsentirety.

FIG. 4I shows the front view of a RID circuit according to anotherembodiment. Rather than inductors 112, 114 mounting to the bottom of thehousing 402, the inductors 112, 114 mount to the side of the housing402.

In order for the magnetic fluxes generated by adjacent array elements toproduce voltages of opposite sign in the RID circuit loops, as providedin Equation 2, all four inductors 112, 114, 122, 124 should be wound inappropriate directions where (i) two of the four inductors are woundclockwise and the other two inductors are wound counterclockwise or (ii)all of the inductors are wound in the same direction. The variouswinding orientations of the four inductors are provided in Table 1.

TABLE 1 Topology of RID Circuit shown in FIG. 1 Inductor Inductor 122Inductor 124 (Array Inductor 112 Inductor 114 (Array Element 1) (RIDCircuit) (RID Circuit) Element 2) Winding Clockwise Clockwise Counter-Counter- Direction clockwise clockwise Clockwise Counter- ClockwiseCounter- clockwise clockwise Clockwise Counter- Counter- Clockwiseclockwise clockwise Counter- Clockwise Clockwise Counter- clockwiseclockwise Counter- Clockwise Counter- Clockwise clockwise clockwiseCounter- Counter- Clockwise Clockwise clockwise clockwise ClockwiseClockwise Clockwise Clockwise Counter- Counter- Counter- Counter-clockwise clockwise clockwise clockwise

As indicated, to construct an RID circuit 102 that does not disturb theB₁ magnetic field of the array elements, the resonant frequency ω₀ ofthe RID circuit 102 has to be sufficiently apart from the resonantfrequency ω_(L) of the array elements 104 (i.e., ω₀<ω_(L)), and the RIDcircuit 102 has to be physically small in size. To satisfy bothconditions, the coupling coefficient k₀ has to be sufficiently large, asboth factors depend on k₀, as provided in Equations 5 and 6.

FIG. 4J illustrates a transceiver phased array decoupled with theresonant inductive decoupling circuit 102 according to the illustrativeembodiment. In the figure, the transceiver phased array 100 includes tworows of four array elements 104. A resonant inductive decoupling circuit102 is employed between each of the adjacent array elements 104. Asshown, 18 RID circuits are employed for the 2×4 array. It should beappreciated that the various embodiments may be applied to transceiverphased arrays having other numbers of array elements using appropriatenumbers of RID. For example, the addition of four-elements to each row(i.e., 16-coil array arranged as a 2×8 array) increases the number ofneighboring pairs to 40. The addition of a third-row of eight elements(i.e., 24-coil array arranged as a 3×8 array) increases the number ofneighboring pairs to 72. For a 32-coil array having a 4×8 arrangement,104 RID circuits may be employed.

The resonant inductive decoupling circuit 102 may be employ to decoupleoverlapping or non-overlapping array elements 104. FIG. 4K is a diagramillustrating the resonant inductive decoupling circuit 102 decoupling apair of non-overlapping array elements 104. FIG. 4L is a diagramillustrating the resonant inductive decoupling circuit 102 decoupling apair of overlapping array elements 104. The relevant portion of theresonant inductive decoupling circuit 102 of FIGS. 1 and 6 are shown inthe dotted-line box 402.

FIG. 4M is a diagram of a pair of array element 104 and a resonantinductive decoupling circuit 102 in relation to a sample 110. Asindicated, the resonant inductive decoupling circuit 102 should besufficiently small to not cause distortions to the B₁ magnetic field ofthe array elements. To satisfy the size constraints, the size 404 of theinductors 112, 114 may be less than 30 percent of the distance 406between the array elements 104 and the sample 110.

Performance Comparison to Other RID Circuits

Through experimentation, it is observed that in spite of being muchsmaller in size, the RID circuits 102 according to the illustrativeembodiment have substantially larger k₀ values compared to other RIDcircuits known in the art. Table 2 provides the parameters of the RIDcircuit 102 of the present embodiment and parameters for other RIDcircuits.

TABLE 2 Type Inductor Size k₀ f₀, MHz ξ Q₀ Type I RID Circuit Dia. 4 mm0.14 259 0.13 300 Topology 1 Dia. 16 mm 0.05 293 0.017 280 Topology 1Dia. 22 mm 0.06 289 0.03 325 Topology 1 Dia. 28 mm 0.09 280 0.064 440Topology 2 15 × 60 mm 0.06 288 0.034 380 Topology 3 20 × 20 mm 0.04 2940.013 400

FIGS. 5A-C and FIGS. 6A-6C demonstrate several examples of resonantinductive decoupling circuits known in the art. Specifically, FIG. 5A isa diagram of a Topology 1 RID circuit, of Table 3, described inAal-Braij et al, A novel inter-resonant coil decoupling technique forparallel imaging, Proceedings of the 17th Annual Meeting ISMRM,Honolulu, USA, 2974, (2009). FIG. 5B is a diagram of a Topology 2 RIDcircuit described in Soutome et al, Vertical Loop Decoupling Method forGapped Phased-Array Coils, Proceedings of the 19th Annual Meeting ISMRM,Montreal, Canada, 1859 (2011). FIG. 5C is a diagram of a Topology 3 RIDcircuit according to an alternate embodiment.

Alternative Embodiment of Type I RID Circuit

FIG. 7 illustrates a resonant inductive decoupling (RID) circuit 702according to an alternate embodiment. The resonant inductive decouplingcircuit 702 includes two inductors 704, 706 that form a single loop inseries with a capacitor 708 to generate a single current 710. Theinductors 704, 706 couple to inductors 712, 714 formed in each of thearray elements 104. The orientation of the inductors 704, 706, 712, 714may be wounded such that the fluxes generated by adjacent array elementsproduces voltages of opposing sign in the RID circuit, therebygenerating two opposing currents in the single loop of the resonantinductive decoupling circuit 702.

To do so, all four inductors 704, 706, 712, 714 should be wound inappropriate directions where at least one of the inductors is wounddifferently from the other three inductors. The various windingorientations of the four inductors are provided in Table 2.

TABLE 2 Topology of RID Circuit (Type I) shown in FIG. 7 InductorInductor 122 Inductor 124 (Array Inductor 112 Inductor 114 (Arrayelement 1) (RID Circuit) (RID Circuit) Element 2) Winding ClockwiseCounter- Counter- Counter- Direction clockwise clockwise clockwiseCounter- Clockwise Counter- Counter- clockwise clockwise clockwiseCounter- Counter- Clockwise Counter- clockwise clockwise clockwiseCounter- Counter- Counter- Clockwise clockwise clockwise clockwiseCounter- Clockwise Clockwise Clockwise clockwise Clockwise Counter-Clockwise Clockwise clockwise Clockwise Clockwise Counter- Clockwiseclockwise Clockwise Clockwise Clockwise Counter- clockwise

Type II RID Circuit

When wound differently (i.e., having even numbers of the clock-wise andcounter-wise inductors), the resonant inductive decoupling (RID) circuitof FIG. 7 may be configured as “a Type II RID Circuit.” In a Type I RIDcircuit (shown in FIG. 2), the array elements generate magnetic fluxesthat produce voltages of opposite sign. However, in the Type II RIDcircuit, the array elements generate magnetic fluxes that producevoltages of the same sign in the RID circuit. FIG. 8 is an electricaldiagram showing the Type II resonant inductive decoupling circuits whenwound with an even number of clock-wise and counter-wise inductors. Thesolved Kirchhoff equations of the Type II resonant inductive decouplingcircuit is shown in Equation 8.

$\begin{matrix}{\begin{pmatrix}V_{1} \\V_{2}\end{pmatrix} = {\begin{pmatrix}{Z_{1} + \frac{\omega_{L}^{2}M_{0}^{2}}{Z_{0}}} & {{{- j}\;\omega_{L}M} + R_{12} + \frac{\omega_{L}^{2}M_{0}^{2}}{Z_{0}}} \\{{{- j}\;\omega_{L}M} + R_{12} + \frac{\omega_{L}^{2}M_{0}^{2}}{Z_{0}}} & {Z_{2} + \frac{\omega_{L}^{2}M_{0}^{2}}{Z_{0}}}\end{pmatrix}\begin{pmatrix}I_{1} \\I_{2}\end{pmatrix}}} & \left( {{Equation}\mspace{14mu} 8} \right)\end{matrix}$

Solving for the off-diagonal elements for a Type II RID circuit ofEquation 8 yields Equation 9.

$\begin{matrix}{{{- j}\;\omega_{L}{L\left( {k + \frac{k_{0}^{2}}{2\xi}} \right)}} + R_{12} + {\frac{R}{4}\frac{k_{0}^{2}}{\xi^{2}}\frac{Q}{Q_{0}}}} & \left( {{Equation}\mspace{14mu} 9} \right)\end{matrix}$

Therefore, the reactive component of the Z₁₂ can be cancelled when Δω<0,which occurs when ω₀>ω_(L). As indicated, the array elements generatemagnetic fluxes that produce voltages of the same sign in the Type IIRID circuit. This is shown in Equation 8. As such, the inductors of theType II RID circuit may only add to the R₁₂ since both resistivecomponents have the same sign. Nevertheless, the mutual inductance iseliminated when k₀ ²=−2kξ. Thus, the Type II RID circuit may also beused for compensating for the mutual reactance between a pair of arrayelements by satisfying the condition, ξ<0, which occurs when ω₀>ω_(L).Here, ξ should also be sufficiently large so as to not increase theresistive coupling. This can be achieved if the RID circuit has asufficiently large coupling coefficient k₀. The Type II RID circuit maybe employed to decouple a transceiver phased array where the resistivecomponent is small and can be neglected thus requiring only minimizationof the inductive (i.e. reactive) coupling.

Q-Factor and Voltage Estimation

Currents induced in the inductors of the resonant inductive decouplingcircuit 102 may generate losses, which may spoil the unloaded Q-factorQ_(U) of the array elements 104, which may affect the performance of thetransceiver phased array 100. Changes in the Q_(U) may be estimated frominduced changes in the impedance values Z₁, Z₂ of the array elements 104using Equations 2 and 8. The estimate may be expressed as ΔZ, providedin Equation 10.

$\begin{matrix}{{\Delta\; Z} = {{\frac{\omega_{L}^{2}M_{0}^{2}}{Z_{0}} \approx {\frac{\omega_{L}^{2}M_{0}^{2}}{4{\Delta\omega}^{2}L_{0}^{2}}\left( {R_{0} - {2j\;{\Delta\omega}\; L_{0}}} \right)}} = {{\frac{k^{2}}{k_{0}^{2}}\frac{Q}{Q_{0}}R} - {j\mspace{11mu} k\;\omega_{L}L}}}} & \left( {{Equation}\mspace{14mu} 10} \right)\end{matrix}$

The new unloaded Q-factor QU′ may be estimated as Equation 11.

$\begin{matrix}{Q_{U}^{\prime} = {Q_{U}\frac{1 - k}{1 + {\frac{k^{2}}{k_{0}^{2}}\frac{Q}{Q_{0}}}}}} & \left( {{Equation}\mspace{14mu} 11} \right)\end{matrix}$

Additionally, the voltage generated across the capacitors 116, 708within the resonant inductive decoupling circuit 102, 702 may be highand may be controlled by the values of the capacitors and their number.From Equation 1, the current I₀ for the Type I RID circuit may beexpressed as Equation 12.

$\begin{matrix}{I_{0} = {{{\frac{j\;\omega\; M_{0}}{Z_{0}}\left( {I_{2} - I_{1}} \right)} \approx {\frac{k_{0}}{2\xi}\sqrt{\frac{L}{L_{0}}}\left( {I_{2} - I_{1}} \right)}} = {\frac{k}{k_{0}}\sqrt{\frac{L}{L_{0}}}{\left( {I_{2} - I_{1}} \right).}}}} & \left( {{Equation}\mspace{14mu} 12} \right)\end{matrix}$

In the case of equal current amplitudes (i.e. I₁=I₂=I), the amplitude of

${I_{0} \approx {\frac{k}{k_{0}}\sqrt{\frac{L}{L_{0}}}I\;{Sin}\;\varphi}},$where φ is the phase shift between I₁ and I₂.

Decoupling of Double-Tuned Transceiver Phased Arrays

The method described above can also be used to decouple double-tunedsurface coils (i.e., array elements). Double-tuned (e.g. ³¹P/¹H)transceiver phased array is beneficial at super-high magnetic fields(>7T) for X-nuclei imaging and spectroscopy. See, for example,Avdievich, Transceiver Phased Arrays for Human Brain Studies at 7T,41(2) Appl. Magn. Reson., 483-506 (2011). It drastically improved thecoil transmit efficiency, the homogeneity, and the SNR at the higher ¹Hfrequency in comparison with a double-tuned volume coil. At the sametime, the phased array is observed to provided substantially better, insome instances up to four times, peripheral SNR at ³¹P frequency whilehaving similar (i.e., 20% better) SNR near the array center. Individualelements of a double tuned phased array may be realized using either asingle double tuned coil resonating at two frequencies or two separatecoils located closely to each other.

The single double-tuned coil resonating at two frequencies is describedin Schnall et al, A new double-tuned probe for concurrent ¹ H and ³¹ PNMR, 65 J. MAGN. RESON. 122-129(1985), which is incorporated byreference herein in its entirety. Two separate resonance surface coilsresonating at two frequencies are described in Klomp et al,Radio-frequency probe for 1H decoupled ³¹ P MRS of the head and neckregion, 19 MAGN. RESON. IMAG. 755-759 (2001) and Dabirzadeh et al, Trapdesign for insertable second-nuclei radiofrequency coils for magneticresonance imaging and spectroscopy, 35B(3) Conc. Magn. Reson. B: Magn.Reson. Eng. 121-132 (2009), which are incorporated by reference hereinin their entirety.

In both cases, the inventors have discovered that there is a benefit ifthe decoupling device is also double tuned. The two current patterns ofthe Type I and Type II RID circuits of FIGS. 2 and 7 may be realizedsimultaneously using a double tuned (resonance frequencies−f₁,f₂) 2-modedetuning coil.

FIG. 9 presents a low-pass embodiment of a double tuned detuning-coilaccording to an embodiment. The lower frequency Type II RID circuit(resonance frequency f₁) produces loop currents flowing in the samedirection, and the higher frequency Type I RID circuit (resonancefrequency f₂) generates currents in opposite directions.

The modes may be utilized to decouple a pair of double-tuned surfacecoils when each mode is independently tuned. The higher frequency modewith opposite currents in the loops may be used to decouple the arrayelements at ¹H frequency under conditions f₂<f_(1H), while the lowerfrequency mode may decouple the array elements at X-nuclei frequencyunder conditions of f₁>f_(x), where f_(x) and f_(1H) are X-nuclei and ¹Hare Larmor resonance frequencies. FIG. 10 is an electrical schematic ofa double-tuned decoupling circuit.

The variable capacitor 1002 for f₁-tuning affects both modes while thef₂ capacitor 1004 tunes only the higher frequency mode. By varying bothof them iteratively, a pair of array elements may be detuned at bothfrequencies.

In an alternate embodiment, the high-pass double-tuned decoupling coilmay be used to decouple double-tuned surface coils. Here, the Type I RIDcircuit mode (i.e. f₁>f₂) compensates for the lowest frequency and isused for decoupling at the X-frequency. Consequently, the Type II RIDcircuit mode is used for decoupling at the ¹H frequency. A selectionbetween the low and the high pass decoupling structures may bedetermined by the capabilities of the Type I RID circuit in compensatingfor the resistive component R₁₂ of mutual impedance Z₁₂.

FIG. 11 is an electrical schematic of a double-tuned decoupling circuitfor a double tuned phased array 1102. The double-tuned phased arrayincludes a first pair of array elements 1104, 1106 to operate a firstfrequency and a second pair of array elements 1108, 1110 located closelyto the first pair to operate at a second frequency.

Decoupling Validation

To demonstrate the Type I and Type II RID circuit and verify theconcepts, several 298-MHz (¹H frequency at 7T) two-array elements 104were constructed with RID circuits 102 as well as with conventionalnon-resonant inductive decoupling circuits for comparison. Thesetransceiver phased arrays were built using non-overlapped rectangularsurface coils (i.e., array element) of the same size (7.5 cm×9 cm) witha 13 mm gap between adjacent (Δn=1) coils. Each surface coil was formedfrom copper tape (6.4 mm width) with six capacitors (100C series,American Technical Ceramics, Huntington Station, N.Y.) uniformlydistributed along the coil's length. All the coils were individuallytuned and matched using variable capacitors (Voltronics, Denville,N.J.). The RID coils (4 mm ID) were built using 18-gauge copper magnetwire (diameter 1 mm) and positioned at ˜10 mm distance from the surfacecoil plane to increase the separation from the sample.

Additionally, a 16-element single-row (1×16) array consisting of smaller(5.6-width and 9 cm-length) overlapped rectangular array elements wasconstructed. FIGS. 12A and 12B illustrate the constructed 16-elementsingle-row transceiver phased array. FIG. 12A shows the back side of the1×16 phased array with the top cover removed. FIG. 12B shows the frontside. The schematic of the transceiver phased array is provided in FIG.3.

To ensure that the RF magnetic field produced by RID circuit is welllocalized and does not perturb the B₁ magnetic field of the arrayelements within the sample, a transmitted B₁ maps (phase and amplitude)is measured according to Pan et al, Quantitative spectroscopic imagingof the human brain, 40 MAGN. RESON. MED. 363-369 (1998), which isincorporated by reference herein in its entirety. The B₁ maps producedby array elements decoupled with the RID circuits were compared to theB₁ maps obtained by the array elements being decoupled with conventionalnon-resonant inductive decoupling. It is noted that the conventionalnon-resonant inductive decoupling is observed to not significantlyperturb the RF field profile. The conventional non-resonant inductivedecoupling was described in Avdievich et al, Short Echo SpectroscopicImaging of the Human Brain at 7T Using Transceiver Arrays, 62 MAGN. RESMED. 17-25 (2009) and Avdievich, Transceiver Phased Arrays for HumanBrain Studies at 7T, 41(2) APPL. MAGN. RESON. 483-506 (2011).

To mimic head loading conditions, two phantoms were constructed. Bothphantoms are filled with NaCl and sucrose in water. The phantom has beendescribed in Beck et al, Tissue-equivalent phantoms for highfrequencies, 20B(1) CONC. MAGN. RESON. B: MAGN. RESON. ENG. 30-33(2004), which is incorporated by reference herein in its entirety.

The percentages by weight were measured at 41.7%, 56.3% and 2.1% forwater, sucrose and NaCl, respectively. The conductivity and thedielectric permittivity measured 0.57 S/m and 52 respectively, whichapproximates that reported for the human head at 300 MHz (1H resonancefrequency at 7 T). The two-coil arrays were evaluated using a 2.0 Lspherical phantom (16 cm dia.). The 1×16 array was evaluated using acylindrical phantom with an elliptical cross-section (14 cm×17 cm). Withthe described solution this provides loading similar to that of anaverage sized human head. Coupling coefficients k and k₀ were estimatedas previously described (27). Q-factors of RIDs were estimated from thefrequency dependence of S12 and measured using a weakly coupled pair ofpick up coils (28). Q-factors of the surface coils were evaluated usingthe frequency dependence of S11 (28). For the 1×16 array QU ofindividual surface coil elements measured 270. QL measured on an averagesize human head varied from ˜70 (Q_(U)/Q_(L)=3.9) for the posteriorcoils (closest to the head) up to ˜100 (Q_(U)/Q_(L)=2.7) for theanterior coils (furthest from the head).

All data were collected using a 7 Tesla Agilent Technology system. Totest the coil performance, gradient echo images (256×256×13 slices) froman adult subject and a phantom were collected using 2/8 mm slicethickness/gap, 19.2 cm×19.2 cm field of view (FOV), TR=400 ms, nominalflip angle 15°. B₁ maps of the individual coils (single coiltransmitting) or the combined array (all coils transmittingsimultaneously) were collected using a rapid gradient echo dual anglemethod (25) with 64×64 resolution, TR=1 s, 5/5 mm slice thickness/gapcentered on the matched gradient echo images. Human data was acquiredunder approval of local IRB.

Test Observations

The geometry of the resonant decoupling circuit has been optimized tonot disturb the profile of RF magnetic field B₁ produced by a pair ofarray elements 104. The RID circuits of FIGS. 5A, 5B and 5C wereconstructed. The Type I RID circuit was positioned, as shown in FIG. 5C,perpendicularly to the array element's plane to minimize distortion ofthe B₁ field. The assumption is that the distortion of the B₁ fieldproduced by the decoupling coil is mostly happening along z-axisparallel to the surface coil plane and does not contribute to the MRsignal. The inner diameter of the decoupling circuit of the RID circuitof FIG. 5A is measured at 22 mm, the k₀ is measured at ˜0.06, and ξ is˜0.03. To produce similar k₀ value, the decoupling circuit of FIG. 5B ismeasured at 15×70 mm², and decoupling circuit of FIG. 5C is measured at26×20 mm². From experimentation, the three decoupling circuits of FIG.5A-5C were shown to disturb the B₁ magnetic field profile in the arealocated near the center between two surface coils and close to thesurface coil's plane. As an example, FIG. 15A shows the axial B₁ mapsobtained using ¹H (298 MHz) 2-coil arrays with the resonant inductivedecoupling shown in FIG. 5A and the conventional inductive decouplingfor three slices separated by 20 mm and located near the coil center.

It was also observed that the presence of the resonant decouplingcircuit (FIGS. 5A-C) also strongly affected the surface coil loading.For example, loaded Q-factor QL increased from 30 to 53 for a two-coilarray with the resonant decoupling shown in FIG. 5A loaded with the“braino” phantom. The increase is in comparison to an array withconventional inductive decoupling. FIG. 13 is a plot illustrating thedependence of the loaded Q-factor Q_(L) on distance between the phantomand the surface coils. The figure was measured using the 2-coil arraydecoupled using (i) a non-resonant inductive decoupling circuit(measurement 1302), (ii) the optimized RID circuit 102 (measurement1304), and (iii) the 16 mm “flat” RID circuit of FIG. 5A (measurement1306).

It was also observed that simply decreasing the sizes of the decouplingcoils did not minimize B₁ distortion. Decrease of the size of thedecoupling coils leads to the decrease in k₀ and according to Equation 4to decrease in ξ value. Even for smaller decoupling coils, distortionsof the B₁ magnetic field as well as change in QL increased when theresonance frequency ω₀ approached the ω_(L) value. To decrease the sizeof the decoupling coils without decreasing k₀ and ξ values, the geometryof the decoupling circuit is modified.

It was observed that the resonant inductive decoupling circuit 102compensates for both components of the mutual impedance between thearray elements 104 and does not disturb the B₁ magnetic field producedby the array elements 104. The resonant inductive decoupling circuit 102had a smaller size inductor (loop ID=4 mm) and produced a substantiallylarger k₀ (k₀ measured being 0.14) and ξ values (value=0.13).Additionally, using the resonant inductive decoupling circuits 102, theB₁ maps (both amplitude and phase) obtained were observed to bepractically identical to B₁ maps obtained using conventional inductivedecoupling.

Cancellation of the cross-talk between array elements 104 using theresonant inductive decoupling circuit 102 was also verified. FIG. 14shows results obtained for ¹H 2-coil array with the surface coils.Sub-plot A (1302) shows a measurement when the transceiver is unloadedand coupled. Subplot B (1304) shows a measurement when the transceiverphased array is loaded and decoupled using a common inductive decouplingmethod, which compensates merely for the reactive component. It wasobserved that when the array was loaded with a phantom located 4-5 cmaway, the decoupling does not produce a result better than −15 dB.Subplot C (1306) shows a measurement when the transceiver phased arrayis loaded and decoupled using the resonant inductive decoupling coil102. It is observed that under the same measurement condition, adecoupling better than −30 dB was obtained.

FIG. 15B shows the B₁ ⁺ maps of individual array element 104 decoupledwith the resonant inductive decoupling circuit 102. As observed, thearray elements 104 have excellent decoupling to adjacent array elements.

The resonant inductive decoupling circuit 102 was verified on an 8-coil(1×8) ¹H transceiver phased array circumscribing the entire head. It isobserved that the decoupling was better than −27 dB for all adjacentsurface coils and better than −20 dB for all surface coils. Themeasurement was performed on average-sized human head. FIG. 16A shows animage of a human patient scanned with the transceiver phased array 100decoupled with the resonant inductive decoupling circuit 102 accordingto the illustrative embodiments. FIG. 16B shows an axial B₁ ⁺ map of thearray elements 104 of the transceiver phased array 100 corresponding tothe scanned image of FIG. 16A. As shown, the axial B₁ ⁺ map demonstratesvery good homogeneity.

For a double-tuned ³¹P/¹H 3-coil array, the double-tuned decoupling coilyielded decoupling better than −17 dB at ³¹P (120.7 MHz) and better than−22 dB at ¹H (298 MHz) frequencies between all surface coils in thearray. FIGS. 17A-C show axial B₁ ⁺ maps of individual surface coils ofthe ³¹P/¹H array obtained at 298 MHz decoupled with the resonantinductive decoupling circuit according to the illustrative embodiment.

FIG. 17D shows axial B₁ ⁺ maps for individual surface coil elements ofthe transceiver phased array of FIGS. 12A and 12B configured with theresonant inductive decoupling circuit according to the illustrativeembodiment. The axial B₁ ⁺ maps illustrate good decoupling between theindividual array elements. FIGS. 17E and 17F show the axial image andcorresponding B₁ ⁺ map obtained using the 16-coil (1×16) overlappedarray. Homogeneity was evaluated as the standard deviation of the B₁ ⁺over the entire slice and measured 9.2%.

While examples of resonant inductive decoupling have been describedpreviously, such circuits compensate only for reactive component ofcoupling. Additionally, all these setups substantially perturb thesensitivity profile of the B₁ magnetic field due to large size of thedecoupling elements and the close proximity between the resonantfrequencies of the array elements and the resonant inductive decouplingcircuit. Therefore the performance of such arrays is inferior to atransceiver phased array configured with resonant inductive decouplingcircuits according to the illustrative embodiment.

Additionally, correcting this requires shifting the resonance frequencyof the RID circuit significantly below that of the array element. Thisrequires increasing the coupling coefficient k₀ while decreasing thephysical size of the circuits. This condition cannot be fulfilled usingconventional designs. See, for example, Aal-Braij et al, A novelinter-resonant coil decoupling technique for parallel imaging, 17 PROC.INTL. SOC. MAG. RESON. MED. 2974 (2009); Li et al, ICE decouplingtechnique for RF coil array designs, 38(7) MED. PHYS. 4086-4093 (2011);and Soutome et al, Vertical Loop Decoupling Method for Gapped PhasedArray Coils, 19 PROC. INTL. SOC. MAG. RESON. MED. 1859 (2011).

Also, despite evident benefits of super high fields (≧7T) for humanimaging and spectroscopy, progress has been generally slowed down byhurdles associated with RF detector issues. High-field multi-elementmulti-row transceiver phased arrays, which may potentially provide anappropriate design for such probes, are generally still in the initialdevelopment stage mostly due to issues with decoupling of the individualantennas. For example, all previously described resonant decouplingcircuits have not been able to (1) produce a very localized RF magneticfield that does not interfere with RF field of individual antennas so asnot to spoil array transmission and reception properties, (2) cancel themutual resistance, if present, and (3) be utilized for double-tuning tosimplify the array design.

All the capacitive types of decoupling methods intrinsically requireelectrical connection and, therefore fail to cope with the challenge ofarray segmentation. Conventional inductive decoupling solves that issueof having no electrical connection but is difficult to control distantlyespecially for arrays with larger (>8) number of elements. The resonantinductive decoupling method according to the illustrative embodimentallows for (1) distant and easy adjustment, particularly as the numberof decoupling elements for multiple-row arrays become very large and (2)absence of electrical connection to antennas to simplify arraysegmentation.

Common capacitive techniques have been demonstrated as a decouplingtechnique. See, for example, Adriany et al., Transmit and receivetransmission line arrays for 7 Tesla parallel imaging, 53 MAGN. RESON.MED. 434-445 (2005); Gilbert et al, A Conformal Transceiver Array for 7T Neuroimaging, 67 MAGN. RESON. MED. 1487-1496 (2012); Adriany et al, A32-channel lattice transmission line array for parallel transmit andreceive MRI at 7 Tesla, 63(6) MAGN. RESON. MED. 1478-1485 (2010); andvon Morze et al, An eight-channel, nonoverlapping phased array coil withcapacitive decoupling for parallel MRI at 3 T, 31 CONC. MAGN. RESON. B:MAGN. RESON. ENG. 37-43 (2007).

It has also been shown that inductive decoupling methods may compensatemerely for the mutual reactance. See, for example, Avdievich et al,Short Echo Spectroscopic Imaging of the Human Brain at 7T UsingTransceiver Arrays, 62 MAGN. RES. MED. 17-25 (2009); Avdievich,Transceiver phased arrays for human brain studies at 7T, 41(2) APPL.MAGN. RESON. 483-506 (2011); Shajan et al, A 16-Element dual-rowtransmit coil array for 3D RF shimming at 9.4 T, Proceedings of the 20thAnnual Meeting ISMRM, Melbourne, Australia, 308 (2012); and Roemer etal, The NMR phased array, 16 MAGN. RESON. MED. 192-225 (1990). Forexample, for a pair of overlapped loaded surface coils the ratio ofR₁₂/R, where R is the resistance of each surface coil, can measure from0.2 to 0.4 (15,18). This corresponds to the residual coupling in therange of −14 to −8 dB. See Roemer et al, The NMR phased array, 16 MAGN.RESON. MED. 192-225 (1990); and Wright, Full-wave analysis of planarradiofrequency coils and coil arrays with assumed current distribution,15(1) CONC. MAGN. RESON. B: MAGN. RESON. ENG. 2-14 (2002).

By developing the decoupling method here, the limitation set forth abovemay be overcome and better decoupling obtained by compensating bothreactive and resistive components of the Z₁₂.

The sequence of tuning a RID circuit may be as follows. A first pair ofsurface coils (coil #1 and #2) is provided on the cylindrical surface ofa transceiver phased array. The RID circuit to couple to both of thearray elements and is tuned to adjust the decoupling. An additionalsurface coil (coil #3) may be placed on the cylindrical surface of atransceiver phased array adjacent to the previously provided surfacecoil. If the coil #3 is in the same row of the array, then a RID circuitplaced between coil #2 and coil #3 may be necessary. If coil #3 belongsto the different row, more of RID circuit may be necessary, includingfor example, diagonally adjacent array elements. Each RID circuits maybe adjusted independently.

It should be appreciated by those skilled in the art that the variousembodiments may be applicable to other resonant inductive decouplingcircuits that meet the requirements described herein. For example,Thevinin and Norton equivalence of the various embodiments described inthis application may be similarly decoupled.

It should be appreciated by those skilled in the art that the resonantinductive decoupling circuits described herein and method of usagethereof may be employed for surface coils as well as micro-strips.

The embodiments of the invention described above are intended to bemerely exemplary; numerous variations and modifications will be apparentto those skilled in the art. All such variations and modifications areintended to be within the scope of the present invention as defined inany appended claims.

What is claimed is:
 1. A method of operating a transceiver phased arrayin a magnetic resonance system to produce a dataset of a sample, thetransceiver phase array including a plurality of array elements, themethod comprising: providing a sample within the magnetic resonancesystem; energizing a pair of adjacent array elements of the transceiverphased array to cause transmission of a RF magnetic field by the pair ofadjacent array elements and reception of a resonance signal by the pairof adjacent array elements from the sample, where the pair of adjacentarray elements are used simultaneously for both transmission andreception and have cross-talk characterized as a mutual impedancetherebetween comprising resistive and reactive components, the pair ofadjacent array elements having a resonant inductive decoupling circuitthat compensates for both the reactive and resistive components of themutual impedance between the pair of adjacent array elements duringtransmission and reception; and producing the dataset based on thereceived resonance signal.
 2. The method of claim 1, wherein theresonant inductive decoupling circuit is configured to inductivelycouple to the pair of array elements in a manner that the coupling doesnot distort the transmitted RF magnetic field of the array elementsproduced within the sample.
 3. The method of claim 1, wherein theresonant inductive decoupling circuit comprises: a first small inductorconnected in series with a first array element of the pair of adjacentarray elements; a second small inductor connected in series with asecond array element of the pair of adjacent array elements; and anelectrically insulated resonant coil having a pair of windings includinga first winding coupled with the first small inductor and a secondwinding coupled with the second small inductor.
 4. The method of claim1, wherein the resonant inductive decoupling circuit is configured suchthat flux generated by the pair of array elements produces two currentsof opposing direction in the resonant inductive decoupling circuit, thetwo opposite currents provide conditions for compensating for both thereactive and resistive component of the mutual impedance between thepair of array elements.
 5. The method of claim 3, wherein each of thetwo small inductors of the array elements and each of the pair ofwindings of the electrically insulated resonant coil is each formedhaving two turns to four turns.
 6. The method of claim 1, wherein theresonant inductive decoupling circuit is configured to resonate at aresonant frequency ω₀ sufficiently distant from a resonance frequencyω_(L) of the array elements to compensate for both the reactive andresistive components of the mutual impedance between the pair of arrayelements.
 7. The method of claim 6, wherein the frequency shift,expressed as a difference between ω₀ and ω_(L), is equal to${\frac{k}{2\eta}\frac{Q}{Q_{0}}\omega_{L}},$ where k is the couplingcoefficient between array elements of the pair of array elements, Q₀ isa Q-factor of the resonant inductive decoupling circuit, Q is a Q-factorof the array elements, η is a ratio between (i) a resistive componentR₁₂ between the resonant inductive decoupling circuit and the arrayelements and (ii) a resistance value R of the array elements, and ω_(L)is the resonance frequency of the array elements.
 8. The method of claim6, wherein the resonant inductive decoupling circuit has a couplingcoefficient k₀ with the array element sufficiently large to provide fora sufficiently large difference between the resonant frequency of thearray element and the resonant frequency of the decoupling circuit (i.e.frequency shift) and has a size sufficiently small to not distort a RFmagnetic field of the array elements produced within a sample.
 9. Themethod of claim 8, wherein the sufficiently large coupling coefficientk₀ is equal to ${k\sqrt{\frac{Q_{0}}{\eta\; Q}}},$ where k is thecoupling coefficient between array elements of the pair of arrayelements, Q_(o) is a Q-factor of the resonant inductive decouplingcircuit, Q is a Q-factor of the array element, and η is a ratio between(i) a resistive component R₁₂ between the resonant inductive decouplingcircuit and the array elements and (ii) a resistance value R of thearray elements, and ω_(L) is the resonance frequency of the arrayelements.
 10. A transceiver phased array for a magnetic-resonancesystem, the transceiver phased array comprising: a plurality of arrayelements configured to interact with a sample, the plurality of arrayelements including a pair of adjacent array elements configured forsimultaneous transmission and reception, the pair of adjacent arrayelements having cross-talk characterized as a mutual impedancetherebetween comprising resistive and reactive components; and aresonant inductive decoupling circuit configured to inductively coupleto the pair of adjacent array elements, the resonant inductive couplingcircuit configured to compensate for both the reactive and resistivecomponents of the mutual impedance between the adjacent pair of arrayelements during transmission and reception.
 11. The transceiver phasedarray of claim 10, wherein the resonant inductive decoupling circuit isconfigured to inductively couple to the pair of array elements in amanner that the coupling does not distort an RF magnetic field withinthe sample produced by the pair of array elements.
 12. The transceiverphased array of claim 10, wherein the resonant inductive decouplingcircuit comprises: a first small inductor connected in series with afirst array element of the pair of adjacent array elements; a secondsmall inductor connected in series with a second array element of thepair of adjacent array elements; and an electrically insulated resonantcoil having a pair of windings including a first winding coupled withthe first small inductor and a second winding coupled with the secondsmall inductor.
 13. The transceiver phased array of claim 12, whereineach of the two small inductors of the array elements and each of thepair of windings of the electrically insulated resonant coil is formedhaving two turns to four turns.
 14. The method of claim 6, wherein theresonant inductive decoupling circuit includes a variable capacitor totune the resonant inductive decoupling circuit to resonate at theresonant frequency ω₀.
 15. The transceiver phased array of claim 12,wherein each of the inductors of the pair of array elements isinterleaved with the corresponding winding of the resonant inductivedecoupling circuit.
 16. The transceiver phased array of claim 10,wherein the resonant inductive decoupling circuit is configured suchthat flux generated by the pair of array elements produces two currentsof opposing direction in the resonant inductive decoupling circuit, thetwo currents compensating for both the reactive and resistive componentof the mutual impedance between the pair of array elements.
 17. Thetransceiver phased array of claim 10, wherein the resonant inductivedecoupling circuit is configured to resonate at a resonant frequency ω₀sufficiently distant from a resonance frequency ω_(L) of the arrayelements to compensate for both the reactive and resistive component ofthe mutual impedance between the pair of array elements and not distortthe RF magnetic field of the array element produced within the sample.18. The transceiver phased array of claim 17, wherein the frequencyshift, expressed as a difference between ω₀ and ω_(L), is equal to${\frac{k}{2\eta}\frac{Q}{Q_{0}}\omega_{L}},$ where k is the couplingcoefficient between array elements of the pair of array elements, Q₀ isa Q-factor of the resonant inductive decoupling circuit, Q is a Q-factorof the array elements, η is a ratio between (i) a resistive componentR₁₂ between the resonant inductive decoupling circuit and the arrayelements and (ii) a resistance value R of the array elements, and ω_(L)is the resonance frequency of the array elements.
 19. The transceiverphased array of claim 17, wherein the resonant inductive decouplingcircuit has a coupling coefficient k₀ with the array elementsufficiently large to provide for a sufficiently large frequency shiftof the array element and has a size sufficiently small to not distort aRF magnetic field of the array elements produced within the sample. 20.The transceiver phased array of claim 19, wherein the sufficiently largecoupling coefficient k₀ is equal to ${k\sqrt{\frac{Q_{0}}{\eta\; Q}}},$where k is the coupling coefficient between array elements of the pairof array elements, Q_(o) is a Q-factor of the resonant inductivedecoupling circuit, Q is a Q-factor of the array element, and η is aratio between (i) a resistive component R₁₂ between the resonantinductive decoupling circuit and the array elements and (ii) aresistance value R of the array elements.
 21. The transceiver phasedarray of claim 17, wherein the resonant inductive decoupling circuitincludes a variable capacitor to tune the resonant inductive decouplingcircuit to resonate at the resonant frequency ω₀.
 22. The transceiverphased array of claim 10, wherein the pair of adjacent array elementsare overlapping.
 23. A high-field multi-element multi-rowmagnetic-resonance transceiver-phased array comprising: a plurality ofarray elements forming a first row of array elements and a second row ofarray elements, each array element having at least one adjacent arrayelement having mutual impedance therebetween; and a plurality ofresonant inductive decoupling circuits inductively coupled between pairsof adjacent array elements, each resonant inductive decoupling circuitconfigured to inductively couple to the pair of adjacent array elementsand compensate for both the reactive and resistive components of themutual impedance between the adjacent pair of array elements duringtransmission and reception.
 24. A double-tuned magnetic-resonancetransceiver-phased array comprising: a plurality of array elementsincluding a pair of adjacent double-tuned array elements having mutualimpedance therebetween, each of the double-tuned array elementsconfigured to resonate at two resonant frequencies; and a double-tunedresonant inductive decoupling circuit inductively coupled between thepair of adjacent double-tuned array elements, the double-tuned resonantinductive decoupling circuit comprising: a first small inductorconnected in series with a first double-tuned array element of the pairof adjacent double-tuned array elements; a second small inductorconnected in series with a second double-tuned array element of the pairof adjacent double-tuned array elements; and an electrically insulatedresonant coil having a pair of windings including a first windingcoupled with the first small inductor and a second winding coupled withthe second small inductor.
 25. The double-tuned magnetic-resonancetransceiver-phased array of claim 24, wherein the mutual impedanceincludes both reactive and resistive components, and wherein thedouble-tuned resonant inductive decoupling circuit is configured tocompensate for both the reactive and resistive components of the mutualimpedance between the adjacent pair of double-tuned array elementsduring transmission and reception.